As Donald Trump continues to ponder his choice for secretary of state, and other key foreign policy positions, one thing seems clear: the impact on the peace process between Israelis and Palestinians is likely to be serious and retrograde.

The question now is whether the moribund process, which has weathered presidents both Republican and Democrat since it was sealed in 1993 with the aim of securing a two-state solution, can survive the Trump era at all.

The signs are not encouraging. Israel’s far right has greeted Trump’s success with ecstasy, hailing his promises to recognise Jerusalem as the country’s capital and move the US embassy to the city, as well as suggestions from his team he would not stand in the way of Israeli settlement construction.

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The frontrunners for the secretary of state nomination – Rudy Giuliani and John Bolton – have both been vocal opponents of the idea of a Palestinian state.

Meanwhile his advisers have fuelled a sense of deep confusion by making a series of highly contradictory statements.

What is clear, for all the muddle, is that the centre of gravity in US thinking is lurching from the two-state solution as it has been understood by US politicians and diplomats for more than 20 years seemingly towards one of two extremes: a maximalist pro-Israel administration or, equally risky, a minimalist and disconnected isolationist position.

The dangers of the latter approach were summed up most tellingly in a leaked paper drawn up by two officials at Israel’s ministry of foreign affairs.

They paint a picture of Trump’s possible Middle East policy as incoherent, unsettled, and transactional.

“The diplomatic process between Israel and the Palestinians will not be a top priority for the Trump administration and it’s reasonable to assume this topic will also be influenced by the staff surrounding him and developments in the field,” they wrote last week. “Trump’s declarations do not necessarily point to a coherent policy on this issue.

“As part of his minimal interest in foreign affairs, Trump doesn’t see the Middle East as a good investment and it’s reasonable to assume he will seek to reduce American involvement in the region.”

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The officials are not the only ones to see the risk of Trump’s transactional terms. Some anonymous Israeli officials have warned that the new president might view the peace process “only in terms as currency to pay for things in other fields – for example, in dealing with Russia”.

Beyond lies a more existential question that has been picked up on by several Israeli commentators, among them Ben Caspit in Ma’ariv: whether Trump – beyond his instinctive isolationism – even cares about the issue. “The truth is,” wrote Caspit in the aftermath of Trump’s victory, “he is not even a Republican. Trump is Trump.

“People who have worked with him for years have a sense that he does not particularly like Jews or Israelis. In his genes, he does not have everything that every American politician (including Hillary) has: a deep, automatic commitment to Israel, in any situation and in any weather.”

Another who has cautioned the Israeli right against prematurely celebrating has been the former Obama envoy Martin Indyk, who told Israeli radio: “Trump’s position on Israel is quite unclear. He has said different things to different audiences. I would not depend on a real estate lawyer who works for Trump as necessarily the person who will decide these things.”

That “lawyer” is in fact a pair of them who work for Trump’s business and have advised him on the Middle East: David Friedman and Jason Greenblatt. They represent the more maximalist position that was seized on last week and celebrated by Israel’s pro-settler parties.

They have both said that Trump does not believe Israeli settlements should be condemned as an “obstacle to peace”.

“Somebody has to question why are we creating a Palestinian state that’s going to be another terrorist state,” he said in 2011, welcoming comments by Newt Gingrich that the Palestinians were an “invented people”.

Rudy Giuliani, the former New York City mayor. Photograph: ddp USA/Rex/Shutterstock

“Put Israel aside for a minute. Is it in the interest of the United States of America to create another state where they’re going to be training people to come over here and blow us up? Of course it isn’t.”

Bolton’s stated views do not breach this rightwing consensus. He has suggested the two-state solution is not viable, instead proposing a “three-state solution” that would dump much Palestinian territory on Egypt and Jordan – willing or not.

The maximalist and minimalist positions carry the same inherent risk: that they will push Israel’s most rightwing government even further towards the far-right pro-settlement positions held by the likes of Naftali Bennett’s Jewish Home party.

“Trump’s victory offers Israel a tremendous opportunity to announce that it changes its mind regarding establishing a state of Palestine in the heart of our country,” said Bennett in the immediate aftermath of Trump’s election. “The era of the Palestinian state is over.”

Bennett and likeminded ministers have been as good as their word, pushing new legislation to legalise illegal settlement outposts over even the objections of Israel’s rightwing prime minister, Benjamin Netanyahu. All of this is deeply alarming Palestinian officials.

“There is a feeling of despair,” said one official privately, countering official sentiments of watch and see, adding that whoever Trump selected for secretary of state – and other key foreign policy positions – would be crucial.

“In many ways it is too early to know what it means. Our feeling is Trump doesn’t have an opinion. The first time he spoke on the issue he said the US should be neutral. But if he appoints John Bolton, Rudy Giuliani or Newt Gringrich to secretary of state that would be a disaster for Palestine.”